Can someone please explain to me what this math problem is asking for?

Question

If f(x)={(3,5),(2,4),(1,7)} g(x)= sqrt(x-3)
h(x)={(3,2),(4,3),(1,6)} k(x)=x^2 +5

determine each of the following:
(f o h)(3)=
(f+h)(1)=
(kg)(x)=
(f^(-1))(x)=

I don't know where to begin or what the question is even asking..It's been so long since I've done these problems. If you can tell me what to do that would be great =)

Answer 1

f(x)={(3,5),(2,4),(1,7)} means that f(3)=5, f(2)=4 and f(1)=7
(the same for h(x))

(f o h)(3)
=f( h(3) ) (that's the definition)
=f(2) (because h(3) = 2
=4

(f + h)(1)
=f(1) + h(1) (by definition)
=7 + 6 = 13

(kg)(x)
=k(x) * g(x)
=(x^2+5)*sqrt(x-3)

(f^(-1))(x) is the reverse function of f
e.g. if f(3) = 5 then f^(-1)(5)=3
so: f^(-1)(x)={(5,3),(4,2),(7,1)}

Answer 2

f and h are functions defined only on a few points.
g and k are functions defined on the real line for all x.

(f o h)(3)= dot product of vector at x =3
(3,5)o(3,2) = 3(3) + 5(2) = 9 + 10 = 19

(f+h)(1)= f(1) + h(1) = 7 + 6 = 13

(kg)(x)= k(x)g(x) = (x^2 + 5)sqrt(x -3)

(f^(-1))(x)={(5,3),(4,2),(7,1)}

Answer 3

first find a parabola ax^2+bx+c = 0 that goes through the points (3,5), (2,4), and (1,7) to get f(x).
Do the same to get h(x).
Now you can solve:
(f o h)(3)= by replacing x in f(x) with h(x) and evaluating the result when x = 3
(f+h)(1)= by adding f(x) and h(x) and evaluating at x = 1
(kg)(x)= by multiplying k(x)*g(x)
(f^(-1))(x)= by solving y=f(x) for x

Answer 4

Hi,
Well, the first one:
1) (f o h)(3) is asking for the composition of the functions f(x) and g(x) evalulated at x=3. That means replace each x in f(x) with g(x); then evaluate the result with 3 substituted for x.

2) Add f(x) and h(x) and evaluate the result at x=1.

3) I think you may have mistyped this one.

4) This is asking for the inverse of f(x). There's a cookbook procedure for finding inverses. Look it up in the index of your book.

Hope this helps.
FE.